LCM of 49 and 54
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
It is easy to find the LCM of 49 and 54 with the help of the handy LCM Calculator. You have to enter 44, and 60 as inputs to avail the LCM 2646 as output. Here you can check the answer for Find the LCM of 49 and 54.
What is LCM of 49 and 54
Given Numbers are 49, 54
We can find the LCM of 49, 54 using the brute force method, prime factorization method, or GCD method.
To use brute force method, list the multiples of 49 and 54
Multiples of 49 =49,98,147,196,245,294,343,392,441,490,539,588,637,686,735,784,833,
Multiples of 54 =54,108,162,216,270,324,378,432,486,540,594,648,702,756,810,864,918,
Now, get the least common multiple of 49, 54 which is 2646
So, the LCM of 49, 54 is 2646.
Least Common Multiple (LCM) of 49 and 54 with the help of Prime Factorisation
One method for determining the LCM of 49 and 54 is to compare the prime factorization of each number. You can find the prime factorization for each number by following the instructions below:
Here is 49's prime factorization:
| 7 | 49 |
| 7 | 7 |
| 1 |
Prime factors of 49 are 7.
49 = 72
And this is 54's prime factorization:
| 2 | 54 |
| 3 | 27 |
| 3 | 9 |
| 3 | 3 |
| 1 |
Prime factors of 54 are 2,3.
54 = 21×33
When comparing the prime factorization of these two numbers, look for the highest power to which each prime factor is raised. In this case, the following primary factors must be considered:7, 2,3
.21×33×72 = 2646
This shows that the LCM of 49 and 54 is 2646.
How to Calculate the LCM of 49 and 54 Using Common Multiples
The first step in determining the Least Common Multiple of 49 and 54 is to generate a list of multiples for each number.
Lets look at the multiples of these two numbers, 49 and 54:
Lets look at the first ten multiples of these numbers, 49 and 54:
49,98,147,196,245,294,343,392,441,833 are the first ten multiples of 49.
54,108,162,216,270,324,378,432,486,918 are the first ten multiples of 54.
You can continue to list the multiples of these numbers until you find a match. Once you have found a match, or several matches, the Least Common Multiple is the smallest of these matches. The first matching multiple(s) of 49 and 54, for example, are 588, 833, and 864. 2646 is the least common multiple since it is the smallest.
49 and 54 have an LCM of 2646.
Least Common Multiple of 49 and 54 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 49 and 54, than apply into the LCM equation.
GCF(49,54) = 1
LCM(49,54) = ( 49 × 54) / 1
LCM(49,54) = 2646 / 1
LCM(49,54) = 2646
Related Least Common Multiples of 49
Related Least Common Multiples of 54
Frequently Asked Questions on LCM of 49 and 54
1. What is the LCM of 49 and 54?
The LCM of 49 and 54 is 2646.
2. How to find the lowest common multiple of 49 and 54?
To find the lowest common multiple of 49 and 54, we have to get the multip;es of both numbers and identify the least common multiple in them which is 2646.
3. What are the Factors of 49?
Answer: Factors of 49 are 1, 7, 49. There are 3 integers that are factors of 49. The greatest factor of 49 is 49.
4. What are the Factors of 54?
Answer: Factors of 54 are 1, 2, 3, 6, 9, 18, 27, 54. There are 8 integers that are factors of 54. The greatest factor of 54 is 54.
5. How to Find the LCM of 49 and 54?Answer:
Least Common Multiple of 49 and 54 = 2646
Step 1: Find the prime factorization of 49
49 = 7 x 7
Step 2: Find the prime factorization of 54
54 = 2 x 3 x 3 x 3
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 2646 = 2 x 3 x 3 x 3 x 7 x 7
Step 4: Therefore, the least common multiple of 49 and 54 is 2646.